Please upload the entire plan for better comparisions. Also along with below options
SET STATISTICS IO ON
SET STATISTICS TIME ON
also enable
SET STATISTICS PROFILE ON to compare execution plans, rows returned and subtree cost for each plan.

Tried to do a simple repro of your problem and below are sample script see if they imitate your problem:

update statistics testperformance with fullscan
set statistics profile on
go
set statistics time on
go
set statistics io on
go

select count(*) from testperformance with (index(indcar,indwife))
where
hascar=0 AND haswife=0

select count(*) from testperformance --with (index(indcar,indwife))
where
hascar=0 AND haswife=0

Got almost same time of plans that you had pasted in here.

With index hints provided there seems to be a merge join occuring between different columns and I bet if you looked at the subtree cost of both plans plan with index hints costed higher than default one.

Also CONVERT_IMPLICIT is also present CONVERT_IMPLICIT(int,[globalagg1008],0))) that can impact performance.

The plan with index hints is going to be a CPU hogging one if put under stress test as since it is a merge join we are more on cpu also in some cases there may be sort operations involved prior to merge join.

In SQL Server 2000 earlier version book mark lookups cost are not properly estimaated and we are gradually moving away from bookmark lookups.